Question

standard 15 homework
score: 12.67/21 answered: 14/20
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question 15
write the equation of a graph that is obtained by vertically stretching the graph of ( y=sin (x) ) by a factor
of 3 and shifting it 9 units to the right and 5 units down.
( f(x)= )
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Explanation:

Step1: Vertical stretch

For the function \(y = \sin(x)\), a vertical stretch by a factor \(a\) gives \(y=a\sin(x)\). Here \(a = 3\), so we get \(y = 3\sin(x)\).

Step2: Horizontal shift

A horizontal shift of \(h\) units to the right for the function \(y=f(x)\) gives \(y = f(x - h)\). Here \(h=9\), so we have \(y=3\sin(x - 9)\).

Step3: Vertical shift

A vertical shift of \(k\) units down for the function \(y = f(x)\) gives \(y=f(x)-k\). Here \(k = 5\), so \(y=3\sin(x - 9)-5\).

Answer:

\(f(x)=3\sin(x - 9)-5\)